MCQ
Numerical: Powers, Roots & Indices MCQ - Practice Questions with Answers
Solve 12 Numerical: Powers, Roots & Indices questions for RAS/RPSC preparation.
Practice questions
Q1Among the following numbered statements, which one is incorrect? 1. 3^4 = 81; 2. √144 = 14; 3. 5^0 = 1; 4. ∛125 = 5.
Check each statement separately. For statement 1, 3^4 means 3 × 3 × 3 × 3 = 81, so it is correct. For statement 2, √144 is the number whose square is 144, and 12 × 12 = 144, so √144 = 12, not 14. Statement 3 is correct because any non-zero number raised to the power 0 is 1. Statement 4 is also correct because 5^3 = 125. Therefore, the incorrect statement is 2.
Q2Match each expression with its value: 1. 3^4, 2. √625, 3. ∛216, 4. 5^0.
Evaluate the four expressions one by one, using the exact meaning of each symbol. First, 3^4 means 3 × 3 × 3 × 3 = 81. Next, √625 = 25 because 25 × 25 = 625. Also, ∛216 = 6 because 6 × 6 × 6 = 216. Finally, any non-zero number raised to the power 0 equals 1, so 5^0 = 1. Thus the matching is 1-81, 2-25, 3-6 and 4-1.
Q3Simplify: (2^3 × 2^5) ÷ 2^4.
Use the index laws: when powers with the same base are multiplied, add the exponents; when they are divided, subtract the exponent of the divisor. The base remains 2 throughout, so only the exponents need to be handled. Here, (2^3 × 2^5) ÷ 2^4 = 2^(3 + 5) ÷ 2^4 = 2^8 ÷ 2^4 = 2^(8 − 4) = 2^4. Now 2^4 = 2 × 2 × 2 × 2 = 16. Therefore, the simplified value is 16.
Q4Find the value of 81^(3/4).
Use the rule a^(m/n) = (nth root of a)^m. Here 81^(3/4) means the fourth root of 81, raised to the power 3. Since 81 = 3^4, the fourth root of 81 is 3. Now cube this result: 3^3 = 3 × 3 × 3 = 27. Therefore, 81^(3/4) = 27.
Q5Find the coefficient of √2 in √98 + √50 − √18.
Write each surd as a multiple of √2 by taking out the largest square factor. Since 98 = 49 × 2, √98 = 7√2. Since 50 = 25 × 2, √50 = 5√2. Since 18 = 9 × 2, √18 = 3√2. Now substitute these values: √98 + √50 − √18 = 7√2 + 5√2 − 3√2. Combine the coefficients of the like surd √2: 7 + 5 − 3 = 9. Therefore, the coefficient of √2 is 9.
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More questions
6Simplify: 3√12 + 2√27.
7What is the value of (2^3 × 2^5) ÷ 2^4?
8Match each expression with its value: 1. 4^3; 2. √225; 3. 2^−3. Which matching code is correct?
9What is the value of 2^5 × 2^3 ÷ 2^4?
10Match each expression with its value: 1. 2^5, 2. ∛125, 3. 7^0, 4. √49.
11For the assertion-reason pair, choose the correct code. Assertion: 27^(2/3) = 9. Reason: To find 27^(2/3), take the cube root of 27 and then square it. Code 1: both are true and the reason explains the assertion; Code 2: both are true but the reason does not explain the assertion; Code 3: the assertion is true but the reason is false; Code 4: the assertion is false but the reason is true.
12Simplify: √50 + √18 − √8.